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Regular and Chaotic Dynamics, 2023, Volume 28, Issue 4-5, Pages 578–584
DOI: https://doi.org/10.1134/S1560354723040056 (Mi rcd1222) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Special Issue: On the 80th birthday of professor A. Chenciner

A Remark on the Onset of Resonance Overlap

Jacques Fejozabc, Marcel Guardiade

a Université Paris-Dauphine — CEREMADE (UMR 7534), Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France
b Observatoire de Paris — IMCCE (UMR 8028), 77 avenue Denfert-Rochereau, 75014 Paris, France
c CNRS, PSL Research University, 60 Rue Mazarine, 75006 Paris, France
d Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona, Spain
e Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, 08193 Bellaterra, Spain
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DOI: https://doi.org/10.1134/S1560354723040056
Abstract: Chirikov’s celebrated criterion of resonance overlap has been widely used in celestial mechanics and Hamiltonian dynamics to detect global instability, but is rarely rigorous. We introduce two simple Hamiltonian systems, each depending on two parameters measuring, respectively, the distance to resonance overlap and nonintegrability. Within some thin region of the parameter plane, classical perturbation theory shows the existence of global instability and symbolic dynamics, thus illustrating Chirikov’s criterion.
Keywords: Hamiltonian system, instability, resonance overlap, nonintegrability, Chirikov’s criterion, symbolic dynamics.
Funding agency Grant number
European Research Council 757802
Agencia Estatal de Investigacion 10.13039/501100011033
Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D CEX2020-001084-M
Agence Nationale de la Recherche ANR-CE40-0014
M. Guardia has been supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 757802). This work is part of the grant PID-2021-122954NB-100 funded by MCIN/AEI/10.13039/501100011033 and “ERDF A way of making Europe”. M. Guardia is also supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2019. This work is also supported by the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M). This work is also supported by the project of the French Agence Nationale pour la Recherche CoSyDy (ANR-CE40-0014).
Received: 11.11.2022
Accepted: 09.08.2023
Document Type: Article
MSC: 37J40
Language: English
Citation: Jacques Fejoz, Marcel Guardia, “A Remark on the Onset of Resonance Overlap”, Regul. Chaotic Dyn., 28:4-5 (2023), 578–584
Citation in format AMSBIB
\Bibitem{FejGua23}
\by Jacques Fejoz, Marcel Guardia
\paper A Remark on the Onset of Resonance Overlap
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 4-5
\pages 578--584
\mathnet{http://mi.mathnet.ru/rcd1222}
\crossref{https://doi.org/10.1134/S1560354723040056}
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  • https://www.mathnet.ru/eng/rcd/v28/i4/p578
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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